Running coupling corrections to inclusive gluon production

TL;DR

This paper calculates running coupling corrections for inclusive gluon production in high-energy hadronic collisions, replacing fixed couplings with a complex 'septumvirate' of running couplings, and discusses implications for the k_T-factorization formula.

Contribution

It introduces a novel 'septumvirate' of running couplings for gluon production, extending the small-x evolution framework with complex momentum scales.

Findings

Replaced fixed couplings with seven running couplings in the cross section

Identified complex conjugate momentum scales for the denominator couplings

Provided a conjecture for incorporating running couplings into the full k_T-factorization formula

Abstract

We calculate running coupling corrections for the lowest-order gluon production cross section in high energy hadronic and nuclear scattering using the BLM scale-setting prescription. At leading order there are three powers of fixed coupling; in our final answer, these three couplings are replaced by seven factors of running coupling: five in the numerator and two in the denominator, forming a `septumvirate' of running couplings, analogous to the `triumvirate' of running couplings found earlier for the small-x BFKL/BK/JIMWLK evolution equations. It is interesting to note that the two running couplings in the denominator of the `septumvirate' run with complex-valued momentum scales, which are complex conjugates of each other, such that the production cross section is indeed real. We use our lowest-order result to conjecture how running coupling corrections may enter the full fixed-coupling k_T-factorization formula for gluon production which includes non-linear small-x evolution.